33. Putting a satellite in orbit The strength of Earth's gravitationalfield varies with the distance r from Earth's center, and the magni-tude of the gravitational force experienced by a satellite of mass mduring and after launch ismMGF(r) -Here, M - 5.975 x 104 kg is Earth's mass, G - 6.6720 x10-"N-m² kg is the universal gravitational constant, and r ismeasured in meters. The work it takes to lift a 1000-kg satellitefrom Earth's surface to a circular orbit 35,780 km above Earth'scenter is therefore given by the integral35,76001000MG-dr joules.Work =Evaluate the integral. The lower limit of integration is Earth's radi-us in meters at the launch site. (This calculation does not take intoaccount energy spent lifting the launch vehicle or energy spentbringing the satellite to orbit velocity.)

To write the expression for Earth's gravitational force on two object is, F(r)=mMGr2

Answered: 33. Putting a satellite in orbit The…

Glencoe Physics: Principles and Problems, Student Edition

1st Edition

ISBN:9780078807213

Author:Paul W. Zitzewitz

Publisher:Paul W. Zitzewitz

Chapter7: Gravitation

Section: Chapter Questions

Problem 5STP

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Similar questions

The mean diameter of the planet Mercury is 4.88106m , and the acceleration due to gravity at its surface is 3.78m/s2 . Estimate the mass of this planet.
I0 orbits Jupiter with an average radius of 421,700 km and a period of 1.769 days. Based upon these data, what is tha mass of Jupiter?
Suppose astronomers find an earthlike planet that is twice the size of Earth (that is, its radius is twice that of Earth’s). What must be the mass of this planet such that the gravitational force (Fgravity) at the surface would be identical to Earth’s?
On a planet whose radius is 1.2107m , the acceleration due to gravity is 18m/s2 . What is the mass of the planet?
What is the difference between the force on a 1.0-kg mass on the near side of I0 has mean radius of 1821 km and a mean orbital radius about Jupiter of 421,700 km. (b) Compare this difference to that calculated for the difference for Earth due to the Moon calculated in Example 13.14. Tidal forces are the cause of I0 ’s volcanic activity.
Assuming a circular orbit for the Sun about the center of the Milky Way galaxy, calculate its orbital Speed using the following information: The mass of the galaxy is equivalent to a single mass times that at the Sun (or located 30,000 ly away.
Check Your Understanding Why not use the simpler expression U=mg(y2y1) ? How significant would the error be? (Recall the previous result, in Example 13.4, that the value g at 400 km above the Earth is 8.67m/s2 .)
What is the gravitational acceleration close to the surface of a planet with a mass of 2ME and radius of 2RE where ME, and RE are the mass and radius of Earth, respectively? Answer as a multiple of g, the magnitude of the gravitational acceleration near Earths surface. (See Section 7.5.)
The acceleration due to gravity on the surface of a planet is three times as large as it is on the surface of Earth. The mass density of the planet is known to be twice that of Earth. What is the radius of this planet in terms of Earth’s radius?
When Sedna was discovered in 2003, it was the most distant object known to orbit the Sun. Currently, it is moving toward the inner solar system. Its period is 10,500 years. Its perihelion distance is 75 AU. a. What is its semimajor axis in astronomical units? b. What is its aphelion distance?
An object of mass m is located on the surface of a spherical planet of mass M and radius R. The escape speed from the planet does not depend on which of the following? (a) M (b) m (c) the density of the planet (d) R (e) the acceleration due to gravity on that planet
Tidal friction is slowing the rotation of the Earth. As a result, the orbit of the Moon is increasing in radius at a rate of approximately 4 cm/year. Assuming this to be a constant rate, how many years will pass before the radius of the Moon's orbit increases by 3.84106 m (1%)?

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